Don - I have both the composite and component cables (OEM versions; the 3rd-party "equivalents" were locked-out) and the operation / view is identical with either, with the component having the possibility of providing a higher-resolution signal to inputs in your system that can handle it. I don't have the VGA adapter so I can't compare to it. With either composite or component cable in use, only certain video or photo aps are enabled to port through the cable. The image appears on the TV screen and the controls remain on the 'Pad screen, like you described. However, with aps like Safari and Mail, the entire image remains on the 'Pad screen and nothing is output to the TV.
I presume that would apply for the majority of things one can do on the 'Pad (games?) so I was disappointed a bit when I learned of that limitation with the cables, and re-enthused when I learned in this thread that the HDMI dongle will (apparently) allow the 'Pads native screen for all aps (?? - TBD) to appear on the remote monitor. Will that be true for the original 'Pad as well as iPad2 as Scott mentioned? Time will tell. I expect the original 'Pad will still output in only 720p as you mentioned (HW limitations) whereas the 2 version will accommodate 1080p, but as I mentioned above that won't matter for me. I'm also interested to confirm whether or not the full DD SS signal will port via that connection (assuming the file has it), tho' again that's merely a matter of curiosity. For the foreseable future I don't envision replacing my HD optical devices with a tablet, but that will no-doubt change in time, maybe around iPad4...the one with Flash enabled (for my legacy content) and better on-board audio (at least stereo speakers w/ SRS ??)
One thing I have not resolved yet - When I connect via the component cables directly to my TV, the video image is displayed in OAR. ('Pad is set to "Wide screen", I assume that matters.) But when I connect via my receiver, the image is expanded to fill the 16 x 9 screen. I guess I'll need to drill-down on that input and look for an AR setting, but I don't remember that option being there (?)
Another tidbit: Somewhere I read that the 720p output via the component cable is not absolute even if the source is "HD". IIRC, movies (thus by extension, all videos?) were only output in 420p ?? For the life of me, I can't find that information again to confirm. If that's true then the HDMI dongle could be a real upgrade even for the original 'Pad...